32089360 Engineering Mechanics Question Bank

7/28/2019 32089360 Engineering Mechanics Question Bank

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!ft1 L irt.!' ' :\2 ij -l-t'

A 099

State the e9u|,figns of equilibrium of a coplanar system of forces.Determine the second moment of area of a triangle with respect to the base.Find the resultant of an 800 N force acting to,wards eas.uern direction and500 N force acting towards north eastern direcfon.State Varignon's theorem. 'What is uniform motion?

8.

9.

,/Y.S.n.rech. DEGREE EXAMINATION, NO\BMBER/DECEMBER 2002.First Semester

GE 131 - ENGINEERING MECHANICS(Common to Ail Branches except Marine Engineering)

Time : lhree hours Maximum : 100 marksAlswer AI-L questions.

PART A -(10x 2 =20marks)

3.

4.

5.

6.

7.

9

Determine the position of a particle, whose motion isx = t3 - 3t2 - gt + 12, rvhen veiocity becomes zero.State D'Alembert's principle.What is general piane motion?Define instantaneous centre ol rotation.

given by

10. Define co-efficient of restitution,


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(b) Determine thebeam loaded ascalculations-

13. (a)

vertical components of reaction for the3. Neglect the weight of the bean in theorizontal andshown in Fig.

I

Fig. 3Determine the centroid of the cross-sectional area of an unequal l-sectionshown in Fig. 4

\b

15 cmIIIL

I

cmli

-f- l- --l 30 cmFig. 4

Or(b) A screw jack has square threads of mean dia of 10'0 cm and pitch

1.25 cm. Determine the force that must be applied to the end of 50 cmiever (i) to raise (ii) to lorver a weight of 50 kN' Find the effrciency ofthe jack. ls it selflocking? Assume p = 0 2 '

=--5cm'L-+-IIII

100 N

A 099


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L4. (a) A body is projected at an angle such that its horizontal range is 3 tihesthe maximum height- Find the angle of projection.Or,nft)\L/15. (a)

T\vo bodies weighing 300 N and 450 N are hung to the ends of a ropepassing over ar ideal pulley. With what acceleration the heavier bodycomes down? What is the tension in the string?In the engine system shown in Fig. 5, the crank AB has a constantclockwise angular velocity of 3000 rpm. For the crank position indicated,frnd .(i) the angular velocity ofthe connecting rod(ii) velocity of piston.

Fig. 5Or

The uniform 5 kg rod shown in Fig. 6 is acted upon by 30 N force whichalways acts perpendicular to the bar. If the bar has an initial clockwiseangular velocity ,rr =10 rad,/s when 0 =0o, determine its angularvelocitv at the instant 0 = 90'.

Fig. 6

(b)


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'J,n J.

B.E.lB.Tech. DEGREE EXAMINATION, APRIUMAY 2003.First Semester

GE 131- ENGINEERING MECHANICS(Common to Al1 Branches exclpt Marine Engineering)

Time : Ttrree hours Maximum : 100 marks

4.

2.

1.

Answer ALL questions.PARTA-(10x2=20marks)

A man has a mass of 72 kg i,s standing on a board inclined 20" with thehorizontal. Find the component of man's weight.(a) Perpdhbicular to the plane ofthe board(b) Parallel to the plane of the boiud.A force is represented by a vector form P = (10 r'-- 8j + 14 /z) N. Determinethe projection of this force on a lir,e w-hich oSiginates from (2, -5, 3) and passesthrough point (5, 2, -4).Three couples +16 N.m, -45 N.m and + 120 N.m are acting in the 't1,, yz andrz planes respectively. Determine the magnitude of the resultant vector ofthese three couples.Tw'o wires are attached to a bolt in a fcundation as shor.vn is Fig. e..1.Determine the pull exerted by the bolt on the foundation.

3Aoo rr.t/

Fig Q a.


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5. A semi circular arc having radius 100 mm is located in the rlr plane such tf,atits diameteral edge coincides with the y-axis. Determine the :--coordinate ofits centroid.State and prove parallel axis theoren.

Define co-effrcient of friction and angle offriction.A steel ball is thrown vertically upwards from the top of a building 2b m abovethe ground with an initial velocity of 18 m,/sec. Find the ma_titum heightreached by the ball from the ground.A block having mass of b0 kg has a velocity of 15 m/sec horizontally on asmooth frictionless surface. Determine the value of the horizontar force to beapplied to the btock for bringing the block to rest in 5 seconds.A homogenous circular disk, 1.8 n diameter, has a mass of 36b kg and is madeto revolve_ about an axis passing through its centre by a force of 550 N appliedt-angentiallg- to its circumference. Deternine the angular acceleration oi thedisk.

9.

10.

11. A plate is acted upon by 3-forces and 2 couples as shownDetermine the resultant of these force-coupie system and hndthe point on the r-Axis through which the resultant passes.

PART B-

(5'x 16 = 80 marks)

2 kN{oo'rrj

Q 11.,

5oo ni^^-,.ul* J

fJ 3k^/3oo m^L

in Fig. Q. 11.coordinate r of

{l !!t:L2oo rn nt

Fie.

D 104


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12. (a) A tension ? of magnitude 10 kN is appliedtop A of rigid mast and secured to theFig. Q. 12 (a). Determine moment of thepassing through the base O.

/5 rLI

It_

to the cable attached to theground ai B as shown interrsion ? about the z-axis4yA

tokN

Fig. Q. 12 (b)..1

Lnosv \t-/\----,, ->i.,

9 rn-

2.6 m-

l_

D//t, ,Fig. Q. 12 (a).

Or(b) A unrform bar.43 shown in the Fig. e. 12 (b) has a mass b0 kg andsupports a mass of200 kg atA. A supporting cabre is tied to the bai at cand the other end is fixed to the vertical wariat D. carculate the tensionin the supporting cabre and the magnitude of the reactron ibrce at thepin B. l

D 104


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13' (a) Determine the centroidal coordinates of the area shown in Fig. e. 13with respect to the shown r-y coordinate svstem.

-1J,(() |l111..LI

&D MM

(

ttI

I

\

(b) area of the section shorvn in

o, 'o]-- 60"* *l tFig. Q. 13 (a)

I)eternine the second moment ofFrg. Q. l3 . h , rbour irs base :ri- _, .r.

Fig. Q. 13 ,b)

4


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14. (a)

(b) (i)

A corci is attached to a biock of 50 kg mass, the block is positioned ona 20' incline as shorvn in Fig. Q. 14 (a). The other end of the cord issupporting a cyhnder- If the co-efficient of friction between the block andthe incline is 0.2 and co-efficient of friction between the cord and thecylindrical support surface is 0.3, deiermine the range of mass of cylinderfor which the system is in equilibrium. _-- 0.3

Cylinder

trig Q. 14 (a)

Or

I

II

rIrl

i

"irb

A particle under constant decelerationand covers a dislance ol 20 rneters inmeters in the nexl 5 seconds. Calculatesub,sequenl 3 second-. and the totalparticle befr-,re il comes lo rest

is nioving rn a sti-aighl linethe firsl 2 seconcls ar.rd .10the distancc it covers in thedislance travellcd by lhe

( tjl(ii) A u'heel 1.2 m in ciianeter accclelates unifolmlY fiotn t-est lc

2000 rpm in 20 -.econds. Calculale (1) N,.rrnbcr of r-evoluttons thervheel makes rn atlainlng rls spced ol 2000 r'pm (2 j Angular-acceleration ol lhe rrl-reel and (3) Tanger-rtial r'elocttl of ai point otrthe r-in olthe rvheel. 0.6 seconds ar{ler il has slar-tecl lttrtrt tcst (E)

- ^D, \)L\''- -,.f

D 101


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15. (a) 3? l**,n plalies incrinsd at 30" and 6tt ro ltorizontal aje glz,":ri back to:i::"^:tty" T !\c' Q' 15 (a). tho blt*hs of weight 50 N zta 1o0 N areij::: :" "':j1ul1"" a-nd are connected ir r cord passing ure= z ficlionress pulley' It the coe{ficient of frictioa irrt'oen thle p1u .t '=ot L,locks is0 33' find the resulqqg acceleration of rh.. blocks alrd tlLe tr--,:,2'.,i:t in Lhecord.

"r(,=7 .,

(b)

(ii )

(i)

F-ig. e. 15 (a)Or

,,\-;,]::t^:t".: kg is dr oirped frorn a heirlrt ri 2 rr,,:t-t:t ) I,i-., . '.,-J:-.:,2::'lo^q::rrrrness rs l0 N/rnm. calrrrr.r',.r1r, 1,,.':'.:':. : ... :rri"spllngls ( onrpl.o..^od ,hrough fi rl , . . t r I r r , ., , , , j l, ,,, .:.-T- rr:'l -,"';'^* ]c (l l5 1b) (tr), the blocks ,-\ :rnd li l)L:.. -,:'.:..::... :' ,z:4llt, :' :8 ,r'cspcctrvsly ?he dru^ htt:: i' tr'r'::,.: -. "l --':'--'. "ll:,",* il' ilbLrul tl r axrs of rorrrio^ I rr'J 11. :. -'r\ hr.h iiro hln.l, ,r r ,, , -..\ i:,ii. bpiorp jr rnacl.,..:,r ,1,..,i.: _-., ..

.t s LaJI.'is e

6o15 (b) (ii)

ttt) 1{,t1


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./t. .'--.--l , f-: _-)

A i.20B.E.,B.'lech. DEGREE EXAMINATION, JANUARY 2003'

Common to all Branches except Marine EngineeringGE 131*- ENGINEERING MEOTIANiCS

Time : Three hours Maxianun : 100 malksAlswer AI-L questions-PARTA-(10x2=20marks)lTftoVectolsAandBaregiven.Deterrninct'}reircrossproductandtheunitvector along it. A-2i+3j+k and B=3i-3i+4k'2. Dlstinguish the following types of forces n'ith suitable sketch :(a) Collinear and (b) Co-Planar'3. State ard explain Larni's theorem of triangle larv of equilibrium4. Uncler n'hat conditions do the following coincide :(a) Centre ol mass and CenLre of gravily (b) Centre of gravity and Ccntroidof area.5. what is the conclition in1-enns o{ efficiency for a nachine to be self locking'/6. A palticle, starling lrom rest, moves in a straight line and its acceler:rlion isgr.,".bya-50-35f,m-/sec2wherelisinsec.Deterninethevelocitr,ol.the

particle $'heir it has travelled 52 n'7. A stone is dropped into a wcll and if the splash is heard 2 50 seconds later'determinetheclepthofrvatersurfaceassunringthatthevelocityolsorrndis 330 m/sec.8. Dehne the term co elfrcient of lestltutlon9'statetheequationtoc]eterninetheescapcvelocrtyofasate]]iteloescapefromthe gravitational field of eart'h10. Horv will you calculate the lrnear |estoring {b]lce ol an e}astic n]ater-ral'/

PA11T B - (5 x 16 - 80 marks)11. A three bar pendulum ABCD has thl'ee bars each 2 m in length and rvr:iglung2.5 1.i\ as sl rr,r,,,r, in Frgure 11. It is heid in equiiibriurr b1' applyirrg al-rorizont.al force of 5 kN at the free end. Determine the ar:rgles 0,, 0, ancl 0.n.rade rvilh the vertical.

Figurr: i 1 t5kN


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(a)2" A co-planar parallel force system consisting of three forces acts on a rigidbar Al9 .s shown in Figure 12 (a). Determine the simplest equivalentaction for the force systen- If al additionai force of 10 kN acts along thebar A to B, what would be simplest equivalent action?

B

(b)Or

A force F with a magnitude of 100 N is applied at the origin O of the axesx y z as shown in Figure 12 (b) The linc of action of-F passes througha point A whose co-ordinates are 3 m, 4 m and 5 m. Iletermine(i) the r, y, z scalar components of F (ii) the projection of F,, on F onthe r - y planes (iii) the projection ofF along the line OB '

100 N

R,1 m-- 2ri

30 kN

Figure 12 (b)Calculate the moment of inertia and radius of gy ationlor the sectioned area shown in Figure 13 (a).(a) abcut the

r axl s

Figurc 13 (a)

30 mnr

l-


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G) Determine the product of inertia of the sectionedshown in Figure I3 (b). area about the r-y axes

14. (a)Figure 13 (b)

The vehicle is used to transport supplies to and from the bottom of the25 percent grade as shou'n in Figure 14 (a). Each pair of wheels. one atAand the other at B, has a mass of 140 kg witl a radrus ol glr.ation ofi!9 -"1. The drurn C has a mass of 40 kg and a radius ol glr.ation of100 mni. The total mass ol the vehrcle is 520 kg. The .,ehicln is ."l"usJfrom rest rvilh a resrrai.ing force 7 of 500 N in the control cable whichpasses around the drum and is secured at D. Deterrrrine lhe initialacceleration o of the vehicle. Tl-re rvheels roll without slippinqC

gure 14 (a)

Or(b) Ar object of mass 5 kg is projected rvith a velocity or 20 m/s at an anere of'60" to the horizontal. At the highesl point of its path thr projlctileexplodes and brakes up into tu'o fragments oi'masses 1hg and I1.,.. tt.,..,lragraer-rts separate hor.izont',lly after the explosion. lh. ,,rplosron.eleases irrernal ene.gy s.ch that thc kinetic energy of the s1"tem at rhel'rigfresl poinl is doubled. Calculate the separation be;_weeri t*,.lragments rvhen thcy reach the ground.

Dimensions in millimeters

A 120


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15. (a) A rope is wrapped three and a half times around a cyiinder as shown inFigure 15 (a). betermine the force Z, exerted on the free end ofthe rope'thatisrequiredtosupportalkNweight.ThecoeffrcientoffrictionbJt*e"n the rope and the cvlinder is 0'25'

(b)

Figure 15 (a)Or

Al inextensible cord. going around a homogeneous cylinder A of mass100 kg holds a massless plate B The collar C of mass 30 kg is releasedfrom rest in the position shown in Figure 15 (b) and drops upon the plate'Deterrnine the velocity of the collar when it has descended an additional0.5 m after striking the p1ate. Assume that there is no rebound; that isC and B move downwards locked together and the cord remains taut

Plate BFigure 15 (b)

A 120


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E 114B.E.,1B.Tech. DEGREE EXAMINATION, NO\IEMBEP"DECEMBER 2003'

First SemesterCommon to all Branches except Marine Engineering

GE 131 - ENGINEERING MECHANICSTime . Thrcp hours Maximun : 100 marhs

Answer ALL queslionsPART A - (.10 x.2 - 20 marks)

A for-ce of 500 N fornsaxes. Writa the fbr-ce in 45" and 120'resPecliveiY r.i ith r, r, and "ngles 60",vector- foln.

,2

a

L

5.

{i.

S.

AB

Q

for-ce of nagnitude ?50 N is dir-ected along AB rv]'Lere A t''is (1.4, 1.2. [r) rn. \\rlrle t]ie vector iorm ofthe for-ce10.8,0. 1.2) m and

alonli-the line joinrng P (2. l. 6) rn andfo|ce al:orrt R (7, 10, iJ) mlolce of ntagttrtude 200 N is acting(4, 7, 10) r'r. !-ind the norrent of theA force 110r + 207 5l) N apphed at '4 t3' 0' 2) m rs rroled to PornlB i6. 3. i ) n. Frnd the l'ork done bf ihe folce

are defined lbr a concut-r-cnt ibr-ce sl'srem

in the frrst and four-l]-r quadlanls \\/r'ite

L Explain the tlif{erence betrveen }rinerlatics and kinelics

Horv nan1,- equations of equilibriunalrd coplarrar- force sl'stem?A scni circle of radius o is clefineddorvn its co-ordinates of centr-oidSiale par-al.lel axis theol'en'tState thc lau's of cL-]' fi-ichon

10. Deflne linear rlomenturr and angular momentunr


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r I {"!j? ""l;:ln?:;xJ;wl::fij;;l:,rl"o sockerjoin, ar *s basel1:!t*,: act in a plane parauei rcr r-y pla,.'e. c""]:t:"t 100^ N and 600 lr' andand reaclion at theball and socket joint. pute the lorces in the cablest'

'-r3

Fig Q. ir12 (a) The lever ABC of a machine component is subjecred to for-ce of 1000 A/hrough a tink AD artached ^,;;:;;;:,. ,,g q 12 (a) Compute rheeaction ol the hir.rged support ., g ""Ji";*,,n the hnk CE

lDo

Fie. Q.12 (a)Or2

ri-,:.

PARTB-(5x16=80marks)

\-.tI ooo t't

E 114


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(b) A framo supporied et A and B is subjected io a forcc of 500 N as shorvnin

n:-- ^ 1e rhi comDute th" ;;;#t "t the supporl points for the cases;i", :oi; B go" and o'- 60"

Fig Q 12 (b)13. (a) Locate the centroicl for tl-re plane surface shorvn in Fig Q 13 (a)

I4 n'" n'll_1Q- ,^

lr;" () lll (3)0r

fl

l-0 O"-"r.t\

Fa.- 33*,

24iIv

B 11,1


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(b) Compute theFig" Q. 1s (b) iecon{ moment of arfftoment olarea of surface shown inbout its triilontal cenGoidatthe planeaxis.

3 o*o

3C-r1.,Ij4n-^-t,)I c,'v,l

I4 (a)Fig. e.13 (b)

(i) Define angle of.friction ard angle ofrepose. G)(rr ) A ladder is S ni long and.l,eigl-rs 300 l/. The centr_e ol.grayiiy of therdopr i- 3 n, el,,nir hc J.,rgr6 oi traa,l1- j,'o,. ,',',.' uo,,r,, .r i I n"d.rn. f,...5 ""o,na] u vprr,i, a, wa.l , B ,nd u r .1,.. ..,, ,r,.,n, ,, loo.,t A as shorvn in tl.re Frg e. t4 (a) (ii) D;;;i;.,',t,,. .rf" irerehr upo v']rich a m:rn r.veiqhrnC :90 -A/ .r,, .f "",l ,r,t,iroul making tlreaclder-slip The coelfi cjeni^ol lri "ti"" f,"t*""lr ,r,id". irnd lloor is 0 4nd ladder iop and ri,all rs 0.3' t. l2)

Fig. Q. 14 (a) (ii)Or

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(i)b) A car starts from rest and accelerates uniformly to a speed of80 kmph over a distance of 500 m' Find time and acceLeration'Further acceleration raises the speed to 96 kmph in 10 seconds'Find the acceleration and distance Brakes are applied to bring thecar to rest under uniform retardation in 5 seconds Find thedistance covered during braking' (8)

(ii) A projectile is thrown rvith a velocity of 5 m'/s at an elevation of 60"tothehorizonla].Findtheveloclt'yofanotherprojectilethrownatan elevation of 45" which will have (1) equal horizontal range(2) equal rnaxrmum height and (3) equal time of flight with the frrst'(8)

(a) T\vo blocks of mass 20 kg and 40 kg are connecled bv a rope passing overa friction less pulley as shown in Fig Q 15 (a) Assuming coefficient offriction as 0.3 for all contact surfaces find the tension in the string'acceleration of the system. Also compute the veiocity of the system aftel4 secondi itarting from rest'

Fig. Q 15 (a)Or

15.

(b) An ir-iextensible str-ing passrngFig. Q. 15 (b) joins trvo blocks lffrom rest, deternine t'he velocitY

over a smooth Pul1e1' as shot'n int1-re blocks are leieased sinultaueousll'of biock A after it has moved over 2 m

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arrd the tension in the string- Assume the coefficient of friction at thecontact surface is 0.2. Use energ-y principle.

2WVtr

25" 16

Fig. Q ls (b)

E 114


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li;\__> tl . lE 197B.E./B.Tech. DEGREE EXAMINATION, NOVEMBERiDECEMBER 2003.

Third SemesterMarine Engineering

MV 305 - APPLIED MECI{ANICSTime : 'Ihree hours Ma:siIrrunr : 100 marks

Alswer ALL questions.PARTA-(10x2=20marks)

1. State the dilference between resultant and equilibrant.2 A force of magnitude 100 N makes angles of 30' and 70' with X and Y axesrespectively. What are the scalar components of the lorce along lhe coordinate

axes 13. Dehne angle of repose.4. A body oiu'eight 50 N rests on a horizontal plane whose coefhcient oflriclion is0.38. A lorce of 15 N is applied on the body as shown in Fig. 1. Wr1l t.he bodymove or not? 15N

5Fig. 1

\4hat is meant by'Friction in a machine'? Hor"r is it exprcssed in terms ofvelocity ratio?Whal is a screrv jack? On rvhat principie does il rr,ork?What is poiar moment of inertia? What is its value lor a semrcircular lamina ofrllQlLls r! :Define radius of gyalion. \Vhal is rts value about the cenlroidal a-us for acircul ar plane of dianeter'L)'?Deline angular velocity and ang..rlar acceler-atron. Slate ihe measuling units ofthe same.State the lan of conservalion of energy.

67.

r+"

10


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11.r PART B - (5 x 16 = 80 marks)Find the.resuitant of the space concurrent forces shown in Fig. e 11. Find alsorrs magxttude and direction lvith respect to the X, y and Z axes.

12. (a)

c (-2,-2,-c")Fig. Q 11

For the system of blocks shown in Fig. emove lower block A and the tension infriction at all contact surfaces to be 0.3.12 (a), frnd force P requiredthe cable. Take coefficient toof

(b)Fig. e 12 (a)

OrT\",'o blocks A and B as shown in Fig. e 12 (b) arethe value of P to cause motion to impend if thebetrveen all surfaces is 0 3.

Fig. Q 12 (b)2

tred b1' a str-ing Frndcoelficient of frichon

A ( 5, +,- 2)B C-7,+2,-3>

E 197


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(u) In a simple screw jack, the pitch of the screw is 10 mm and length of thehandie is 450 mm. Find the velocity ratio. Il an effort gf 25 N applied atthe end of the handie can lift a load of 3000 N, find the eificiency of thejack, Also calcuiate the effort wasied in friction ald the frictional load.t)r

(b) (i) What is the advantage of using a double purchase crab instead of asingle purchase crab?(ii) In a double purchase crab, the pinions have 15 and 20 teeth, rvhilethe spur rvheels have 45 and 40 teeth. ltre effort handle is 40 cmlong while tlie effective diameter of the drtm is 15 cm. If theel{'rciency of the crab is 407o, rvhat load will be lifted by an effort of250 N applied at the end of the handte? Alternateiy, if the efficiencyis 5070, flnd the effort required to lift a load of 1500 N. (13)

74 (al Locate lhe centroid and find the moment ol inertia of the plane sectionshown in Fig. Q 14 (a) about its horizonial and vertical centrordal axes.

5o rnmrc'Ci.,.'>


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15. (a) T\ro blocks of weights ?50 N ald 1500 N start from rest as sh'own inFig' Q 15 ttl' fi"a the acceleration of each block and the distancetravelled by ttie ?SO N biock in 2 seconds Also find the tension in thestring'

\

l

)

^"+\r/: 1 (;e"t 1500NA'zoFig. Q 15 (a)

Or(b j ' A b,tll"t of mass 0 05 kg rnoving with a velocity of 120 m/sec hits a bob ofa simple pendulum hJrizontaily as shown ir Fig Q 15 (b) Find the

maximum angie through which the pendulum swings when the bulletgets embeddeti in the bob'

Fig Q 15 (b)

E 197


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J 2L2B.E./B.Tech. DEGREE EXAMINATION, ApAIl,/MAy 2004.

First SemesterGE 131 - ENGINEERING MECI{ANICS

(Common to A-11 Branches except Marine Engineering)

',, .::,,,P

Nlaximum : 100 marks

a bolt A. Deterrnine the magnitudehorizontal.

of

: Three hours

Alsu-er ALL questi ons.PARTA-(10r2=20marks)

A lorce F :700 t + 1500 7= is applied tothe force and the angle it forrns w.ith theDefine principle of transmissibility.State Varignon's theorem.State perpendicular a-ris theoren.Define principal axes and principal moment of inertiaWhat is called the coefficient of static fnction?What are motion curves?Explain dynamic equrlibrium.Statc law of conservation of momentum.What is general plane molion? Give some examples.

Time


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11. (i). PART B - (5 x 16 = 80 marks)

A system of four forces acting on a body is asDeterrr:ine the resultant force and its direction.

shown in Fig. Q. 11

?oo N

(i).(8)

kg(B)

(ii)Fig. e. 11 (i)

Deter-mine the tension in cables A-Blrateshown in Fig. Q. 11 (ii).

and AC required to hold the 40

+o k?Fig. Q. 1i (ii)

J 2\2


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12. (a) A force acts at the origin ofa co-ordinate system in a direction defrned bythe angles 6, = 69.3' and 0" :57.9'. Kaowing that the y component ofthe force is -174 N, determine, (i) the angle 0", (ii) the othercomponents and the magnitude of the force (iii) p16.yss1i.. of this forceon:z plan and its magrritude and (iv) moment of this force about a pointof co-ordinate (2, 3,4) and its magnitude. (16)Or(b) Four for:ces and a couple are applied to aFig. Q. 12 (b). Determine the magnitudeforce - couple system. Also determine thewhere the resultant intersects-

Fig Q 12 (b)For the plane area shown in Fig. Q. 13 (a),

rectangular plate as shown inand direction of the resultantdistance r from o along r axis(16)

locate the centroid of the area.(r6)

Somrn

(a)

loom"n

3oomt'r

5o rnrn

ser^ic"r-cl-

t-6t.r 'r- ?5 -r- 6a.s-fi6 r}'6 rb6

Fig. Q. 13 (a)Or

-T_'.t

?50krJI

I

Ilo---F- II

J 272


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(b) Find the Moment of Inertia of the section shown in Fig. e. 13 (b) abouthorizonta-l and verticar axes through the centroid. Also determine theprincipal mgments of inertia. (16)lornrr\-l k-f

,,- ,

74. (a) Determine the smallest forceFig Q. l rar jf r ir block A rsand (ii) cable CD is removecl

lDo

Fig. Q. 13 tb)P required to move the block Brestrained by cable CD as shownTake g. = 0.30 and ph = 0.25 .

shown inin figure

(l6)

I !'D mm

Ilornrf\xI----t

Fig. Q 14 (a)Or

1 J 2t2


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(b) Alr object is thrown vertically upward with a velocity of 30 nr/s. Fourseconds larer a second object is project vertically upward with a velocityof 40 m/s. Determine (i) the time (after the first object is thrown) whenthe two objects will meet each other in air (ii) the height from the earthat which the two objects will'meet. (16)

15. (a) A 2000 N block is hanging from an in extensible string which is wrappedaround a drum of radius 400 mm rigidly attached to a rvheer. combinedmass moment of inertia of drum and wheej is 20 kg r:n2. At particularinstant as shorvn in Fig. e. 15 (a), the velocity of the biock is 3 m,/sdownrvard. If the friction force opposes the motron by giving g0 N_mcouple on the bearing, find the velocity of the biock arter it has moveclthrough 2 m dor"rnwarcls, use rvork energl, relationship. ( 16)

Fig Q. 15 (a)

,i 272


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(b) A body weighing 1500 N rests on a rough plaroe inclined at f2" to[horizontal. It is puiled up the plane by means of a light flexible rope

Fig. Q. 1s (b)

running parallel to the plane and passing over a light frictiontess pulleyat the top of the plane as shown in Fig. e. 15 (b). The portion of the ropebeyond the pulley hangs vertically down and carries a weight ofB00 N atits end. If the coeflicient of friction for the plane and the body is 0.2, find(i) tension in the rope (ii) a"""1".u on with which the body moves up theplale and (iii) the distance moved by the body ln B seconds after startingfrom rest. riol

J 272


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ec 123B.E, DEGREE E)LAMINATION. APITiIIMAY 2009.

SECOND SEMESTER(Common to ali branches)

GE 204 - ENGINEERING MECHANICSTime : Tllree hours Maximum : 100 marks

Anslver Al-L qriestions-PART A ( 10 v. 2 = 20 marks )

1. State Principle of Transmissibility.2. Define free body djagram.3. S/hat is meant by radius of glralion?4. Horv rvould you frnd out the centroid ofa composite area?5. Define coe{frcient of friction and lirniting friction.6. List any four engineering applications of friction,7- Define unifor:mly accelerated motion.E. Distinguish between curwilinear motion and proiectile motion.9. State work-energy principle.10. Define the term coefficient of restitution.PARTB-(5x16=B0marks)11. (a) Determine the magnitude T of the tension in the supporting cable andthe magnitude of the force on the pin a1, A for the jib crane shown rnFig.1. The beam AB is standard 0.5 m I beam with a mass of 95 kg permeter of length.

;J=:=-==..=---: :1/i--f, , ! i rr---,-,,r' 1-,t. i.,. - rr.li nr i l:;r.-:I tr 1. :i

Fig. 1.Or


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(b) AstringABCDharrgsfrornfixedpoints,AandDcalT)rrngamassofS0kgat B anc{ a mass of m tg tt C'"ai J inclined at 60' to the horizontal' BCrs horizontal and CD i" ltt"fi""a ut 45" to the horizontal Deterrnine the't."".""1" eg, BC, CD and the mass 'm''Locate the centroid of the cross section of an angle 150 bv 100 by 12 mmshown in Fig. 2.

l*- loo mm ----lFig' 2'

OrT)eterrninethemomentofinertia.oftheareashowninFig.3.(i) About the vertical gravity axis YY(ii) About a horizontal axis a-a 50mm below the base'

12. (a)

2mmITv(b)

t.-I 71.2 mmIr -!lir- I'lt z5'-.

50 mm'l-rl50 mml

175 mm

Fig. 3.

2

50 mma-


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A bociy har.'ing a l:rass of 46 kg res'r.s on a horizontal plane as shown inFig. 4 for rvhich p = 0.4. A force P acts on the body an angle of 20'withthe 1-rorizontal. Find its magnitucie lor inpendlng rnotio:t.

Fig. 4.Or

A flexible cable which supports the 100 kg load is passed over a fixedcircular drum shor,r'n in Fig. 5 and subjected to a force P to maintainequilibrium. The coelficient of static friction between the cable and thefixed drum is 0,3.(r) For a =0, determine the mar.imum and minimum values which Prnay have in order not to r"aise or lower the ioad.(ii) For P= 500N, determine the minimum value which the angle cr may

have before the load begins to slip.

Fig. 5.


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(a) T$o automobiies A and -d3 traveling in the same direction in adjacentlanes are stopped at a traffic signal. -As the signal turns green,automobile A acceleraies at a constant tate o{ 2 m-/s2 TVo seconds later',automobile B starts and accelerates at a constant rate of 3 6 m/s2Determine(i) When and where B will overtake A,(ii) The speed of each aui,omobile at that time'

Or(b) The two biocks shown in figrrre 6 are originally at rest' Neglecting themasses of the pulleys and the effect of fnctiol in the pulleys and betweenthe blocks and the incline, determine

Ttre acceleration of each block,The tension in the cable.

(i)(ii)

15. (a)FiS.6. .

A driver of a light truck applies the brakes when traveling 40 km'4rr, itskids 3 m befoie stopping. How far will the truck skid if it is traveling88 km,4r rvhen the brakes are applied?

(b)f)r

Block A has a mass of 3kg and is sliding on a rough horizontal surfacewith a velocity 2 rds when it makes a direct collision with biock B, whichhas a mass o? 2 kg and is originally at rest' If the collision is perfectlyelastic, determine the velocity of each block just after collision and thedistance between the blocks whey they stop sliding The coefficient ofkinetic friction between the blocks and the plane is 0 3'


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J 1,45B.E./B.Tech. DEGREE EXAMINATION, APRILTMAY 2004.

Ttird SemesterMarine Engineering

MV 305 -APPLIED MECHANICS

('rr' x

j:i

fime : T'hree hours

Answer ALL questions.PARTA-(10x2=20marks)

State the equations of equilibrium of coplarrar system of forces.

State the Varignon's theorem.

Maxirnrrm : 100 marks

a point P, whose position vector(8fi'"m)i + (6mm)t - (4mm)A . FindA force-F - (6N)l - (3N)7 (4N)A is actingfrom the origin 'O' of the co-ordinate axes ls

the moment of lhe force about lhe origin.

Define the term 'lir:orting angle of friciron'.

State the theorems of Pappus and Guldinusvolume of a body.

State the Coulomb's law of dry friction.

1.

2.

3.

4

6.

7.

B.

5. to find out the surface area artd

Sketch the arangement of a dilferential pulley biock system.Define the term 'r'adius of glration' of a plalar lamina.


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,ll ; ,$lililil!iL1llt:lltlt :itit1rfl'I.lii''1..i!ri]t:

,*Give an expression for the second moment of area of an equilateasides 'd with resPect to the base'

10. State the law of conservation of momentum ofa body'PARTB-(5x16=80marks)

\A jib crane arm AB shown in Fig' Q 11 is held horizontallv by meansupporting cable BC' Tlle cross=arm AB is a standard 5 m long I beam w'mass of 95 kg per meter of length' Determine(i) the magnitude ofthe tension in the supporting cable BC'(ii) the components ofthe reaction at pin A'

Fig. Q . 11

12. (a) The 50 kg block shown in Fig' Q 12 (a) rests on the horizontal surA force P = 200 N is applied to the block at angle O ' which carr be va

(i) If the block begins to s).ip' when (D is reduced to 30"' calculatcoef{icient of static friction .pr" betn'een the btock and the surfa

11.


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IfP is applied at ar angleat the contact interface. =

45', frnd the friction force developed(8)

Fis'. Q. 12 (a)

Or(b) Ttre horizontai position of the 500 kg rectangular block of concrete is

adjusted by the 5' wedge under the action of the force p. If the coefficientof static friction for the both pairs of wedge surf:Lces is 0.30 and if thecoefficient of static friction between the block ald the horizontalsurface is 0.60, deter-mine the force P required to move the block. RefFig Q 12 (b). (16)

Fig. Q 12 (b)

A. q - q 9' C aj,i. o'a oot o;'-a l , '.'-, , v< :r.5-.k?':-lo;v.ar,oio-- - ) ia. '' '.'r 'r]o:'- e 9,6 d-19 ..r." e- ,' " s '

J j.4s


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13. (a) A flat belt isshown in Fig'50 rnm. Ttre

used to transmit a torque from pulley A to pulit'Q. 13 (a). The radius of pulley A is 100 '"m and th"r o: 'lo-effrcient of static friction is 0'30 and p* is 0'!

torque which cal be transrrritted if the aliowab\(16)etermine the largestbelt tension is 4 kN'

Fig. Q. 13 (a)

Or

(b) A rope is wrapped three and a half times around a cylinder as shown inUt". Q' it (b). D"t"'mi"" the force 7' exerled on

the free end ofthe ropethat is required to support a 1 kN weight The coeffrcient of frictionbetween the rope and the cylinder is 0 25 (16)

Q. 13 (b)4

I

Fig.J r45


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i

14. (a) Find the polar moment of area about the centroid, for the shaded area in(16)Fig. Q. 14 (a).

Fig. Q. 14 (a)

Or

(b) A open carloon box is to be made from sheet metal that is cut as shown inFig. Q 14 (b). Find the second moment of area about the a-res r and 1'passrng througn L, ( 16)l\,\ !ro

oo

(A-il dimensions in mrn)

5

rnff\Fig. Q. 1a (b)

J 145


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15 (a) A 4 kg,.3:1:.;-:ffLffi":Ji:",i,"ffi ;li;:";*n.IlT:F =2ri +(3 -t)j +t"e' nI}u"" "'i_l.*^.,.,^"ttv of the particle at t = 4s' (16)u = -8i+5j -20fr ro-/s' deterro$e the velocity

(b) (i) Ttre speed of a particle is given by v --'k3 + '5t2 'What distancedoes

it travel while i'" "';;";"t""= fto* z ro'/s to 99 ro/s'(8)

(ii) A 5 kg mass hangs from a spring bliance in an elevator whichis

accelerating tn**u at 2'5 mls2 ' Determine the spring ttl"-:reading'

Or

II J1


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K 1"139B.E./B.Tech. DEGREE EXAMINATION, NO\IEMBER'TDECEMBER 2004'

Third SemesterM arine E ngineering

MV 305 - APPLIED MECAANICSfi6e : Three hours Ma-rimum : 100 :larks

Answer ALL questions.PARTA-,]0Y'2=20narks)

1. A force F of magnitude 10 kN starts from a point A (2' 1' - 3) and passesthrougir the point ,ry (6,3, 1) Represer-rt the force in ierms of unit vectols i' Iand lz .

2. State the conditrons necessary for a coplanar non concurrent force system to bein equilibr-iun3. \Vhat is meant b5'. cone of friction?4. \Vhat is a screrv jack? State the principle of rvhicir it lr'orks5. Derive the eqr'ration fbr the maximum elficiency ol a rnachire6. Whai is the chfference belrveen a 'simple rvheei and axle' and a 'cjriferentialrvhec] and a:-le'??. Ilefine polar- rnonent of inertia What is its value for a circular seclion ofradius 40 rnm?L A semicircular larI-lina 1-ras a cliameler of 100 mm \\'hal i'q ii"s radius of pi'ra't'ior-raboul its centroidal axis parallel to i+"s Ciameler?9. A dr-iver rushing at 20 rn/s t-tnds a rnan on the rorrcl 50 m ahead He in''tantlyapplies ttre brakes, so nt to 'top lhe car-rvithin

10 m of the man Calculate thereiarclation ancl the 1'jne taken to slop the car'

I0. State D Alembert's pnnciple \\'l'ry is it cailed principle ol dynan-iic equilibnum'/PAR'f B - (5 r 16 = 80 marks)1l (i) lrL u lifling nachine arr effort of 15 N raised a load of ?50 N \\hal is lhemec]ranical aclt'ant'agc? Frncl lhe velocilw ratio if the efficiencf al thisloacl is 5071 11 on t-hi machine an ellort of 25 N raised :i load oi 1500 N'*hai is tt't" "ittti""ty" i\trat 'uill be the elforl lo raise a load of 500 N?Caiculate th" nr,,J-',l- mechanical advantage and tr-Laxirnum effici( ncy?


42/59

in the member AB and BC for the syste;l(ii) Calculate the forcel'ig. Q. 11 (ii)'

Fig. Q. 11 (ii).

.".it*" t" U" smooth, determine the reactions at a1I points of contact'

\Fig. Q. 12 (a)

rJr'is t-recl to thr,re cables as sho.'vl.reacir cable ri tire baiiool exerts

72. (a) Two homogeneous spherical balls rest between two vertical walls;;;;t;t:t;.-a, r2 ia). The radius of the srr'aller ball is 16 cm and tilt;;; ; i.i"; kN Ttre ratlius of the bigger ball is 24 cm and its weight;HkN. n-'" distance be'uw'een the wails is 72 cm.lss:T11t":l:."^":t'

ib) i\ balloortlensirlrL itl,n Frx O 131h) L)etcrrline. \.'tr.rl loL,r ol 12C0 N "l

Fig. Q 12 (b)2 I{11


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j3. (a) A body of rveigl-rt 100 N is placed on an inciitedthe horizonial. Ijeterrnine the mininun force p

Llirnensions in mmF ig. Q. 1.1 (a)

plane wbjch is at 30" toapplicd parallel to thedown the plane. \4&enwill move uprvards orplanc necessary to prevent the body from slidingP = 40 N up the planc, check whether the bodydownwards in the plane.Or

(b) Delerriine the horizontal force p required for r.vedge B to raise thc biockA of weight 5000 N as shorvn in Fig. e. 13 (b). The rveight of the rvetlgeis negligible and the coefficient of lriction on all surfaces is 0.25.

C

Fig Q 13 (b)14. (a) l-or- the plane section sho,,vn in Fig. e. 1;+ (a), locaie the centroid an;i finilils rlomenl of inet tiil about its cenlroidal ares

| 4-a,IL4IIlB.'I)

I

-I'l irt, co Il-i

I{ i i:J9


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(b) Determine the moment of inertia of the pla-ne section given in Fig. e- f+about axes )Q( ald YY and also the radii of glration about them.

/Dimensions in mm.

Fig. e. 1a (b)T$o identical blocks as shown in Fig. Q. 15 (a) are reieased fromNeglecting the mass of the pulleys and effect of friction. Find :(i) velocity ofblock B after it has moved 2.5 m(ii) the accelerations ofboth blocks(iii) the tension in the cable. .,-'

15. (a)

(bl

3ko

Fig. Q. 15 (a)Or

T\o automobiles A and B are travelling in the same direction, inadjacent hight,ay }anes. Automobile B is stopped rvhen it is passed by A,rvhich t.ravels at a constant speed of 27 kmph. I\vo seconds later,automobile B starls and accelerates at a constanl rate of 0.9 m/sec2.Determine (i) rvhen and rvhere B will overlake A (ir) the speed of B atthat time.

x 1139:


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/-.\_1J{)' L!

R.E.IB.Tech DEGREE EXAMINATION, APRILI\{AY 2005.First Seme,qter

Common to all branches except N{a ne EngineeringGE 131 ENGINEER]NG MtrCHANICS

Tirae : Three houi-s

1.

2_

5.

6.

Alsr'ver ALL questions'PARTA- (10r2- 20marks)

Define Copianar and Non-coplanar forcesExpl:un parallelogram 1aw.What is space diagram and free body diagram?

Maximum : 100 marks

p (2, 3, 4). Determine the moment ofA force F =6i-3_j-2h acts at a Pointthjs lbrco about the point of origrrr'Defrne product of inertia.Give the centroid of quarter circular arc'Explain dry frictlon.

8. The motion of a particle is defined by the relation x - t3 -16t2 - 22 wherc r isexpressed in metre and I in seconds- Determine the acceleration of the particleat f = 3 s-9. A food packet having a mass of 12 kg is dropped at 5 m/s from a very hrghaltitucie. If the atmospheric drag resistance ,F-, is 80 N, deterrnine the velocity

of the food packet when it has fallen 10 m'10. Wrile clown the equation of principle of work and energ-v for a rigid body'


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PART B - (5 x 16 - 8li marks)11. (i) T\'o cablt-'s are tied together at (l and are loaded a-. shownFie. Q. 11 (i). Deterrnine the tension in lhe cablc AC and BC.

600 N

Fig. Q. 11 (i)(ii) A ladder 4 m long leans against a smooth vertical wall at an angle 60'rvith i.he horizontal. The weight of the ladder is 800 N. \\4rcn a pelsonweighing 700 N stands at 1.2 m from the bottom ofthe iadder, the ladderis iust about to slide. Caiculate the coefficient of friction bettveen theladder and the floor. (8)12. (a) Tlree concurrent forces in space F,, F and { are acting atA as shown

in F:ig. Q. 12 (a). An unknown force F, atiached to the system makes theparticle ,4 in equilibrium. Find the magnitude and direction of theforte -F' '16r4 -50NF: = 80NF: = 90N

Fig. Q. 12 (a)Or

2 R 279


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(b) A 200 kN vertical i"1;.iTi-1'A' 3 li; ili""ff l?6 [ll'*:iiffi:"$ro a sl-afr ar B as "hou romenl aboLrt B'ii rTh.r."n,""i"i r""" "otl*d "1 1 1]i,ili::"..:,? :'f; : Xu-" ,,'o*",',t about Bsnallest force applied at ;,Hil ;N;";';;i f*"n ,''rrt act to createf;i 5il 3:i:"JSil'il t;io;ot'* the gi"en svstem orro'"" ut 8116)

Fig Q' 12 G)Locate the centroid ofthe section shown in Fig Q 13 (a)'

@* loc*(Qr'r'a'v-to-'-

?ncs

(16)

13. (a)a.-;r e[z)

tr==-- &o csEi.' 0 13 (a)

OrF-279


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(b) Determine the moment of inertiaabout centroidal X{ and YY axes :f = 0.912 mY -2.25 m'

\.- 1.3^ --+

3oom

of the section shown in Fig. Q. 13 (b)(16)

TI+\

ID.T

Fie Q 13.ft)14. (a) Two vehicles approach each other in opposite lanes of a straighthorizontal roadway as shown in Fig 14 (a) Find the time and positionsatwhichthevehic]esmeetifbothcontinuetomovewithconstantspeed.(16)

4o r*Jkd_

tr/-\

14 (a)(lr

B

F,g.

B27S


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(b) A particle is projected rn air with a velocity fOO "V" "'-td at an angle of 30'wjth the horlzontal' lind (i) the horizontal range (ii) the maximum helght

j (

75. (a) Two bodies oi weight 20 N and 10 N are connected to the two ends of alight inextensible string' passing over a smooth pulley The weight of 20N is placed on a horizontal surface which the weight of 10 N is hanging \tU "-free in air as shown in Fig Q 15 (a) The horizontal surface is a rough $t*'one, having coefficient between the weight 20 N and the plane surfaceequal to 0 3' using Newton's second law of motion determine (i) theacceleration ofthe system (ii) the tension in the string (16)

reached by the particle and (iii) the time of flight

&"e r'l 1,,

tonrl

(16)

15 (b) is subjected to a moment of8 kg block B after it rises 1.30 m(b)

Fig 15 (a)Or

The drum of mass 20 kg shown in Fig'160 Nm. Determine the sPeed of the

R279


50/59

(b) Determine the moment of inertiaabout centroidal lff and y)z axes :i = 0.912mY = 2-25 m.

l


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[--(b) A particle is projected rn air with a velocity 100 m/s and at an angie o130"

rvith the horizontal' lind (i) the horizontal range (ii) the maximum height

15. (a) Tv'o bodies ot weight 20 N and 10 N are connected to the iwo ends of alight inextensible string' passing over a smooth pulley The weight of 20N is placed on a horizontal surface which the weight of 10 N is hanging \!i. ..free in air as shown in Fig Q 15 (a) The horizontal surface is a rough ii"one' having coeffrcient between the weight 20 N and the plane surfaceequal to 0 3' using Newton's second law of motion determine (i) theacceleration oi the system (ii) the tension in the string (16)

reached by the particle and (iil) the 'uime of flight'

&"c N 1.,

loN\

Fig. 15 (a)Or

( 16)

in Fig. 15 (b) is subjected to a moment ofof the 8 kg block B after it rises 1 30 m(b) The

drum of mass 20 kg shown160 Nm. Determine the sPeed

P"219


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si::iijng f lcm Lesi. .isc uorli :L:iti i_.,r c lg1, il.ir.rctlierl lh: rilult lboiri'{.,1'is ?r-;fJ rrul

'l'lr r r':iciru,s oI g-lr.:LLi o n

Flg 15 lb)

il: 2?:)


53/59

,4'i-vlt : ;t?.-N 1215

B.E.,B.Tech' 1)EGRtrE FIX-A'1\{INATION' NO\iEMBEP"DECEI{BER 2004'First Semester

GE 131 - ENGINEERING NIECILANICS(Common to All Branches Except Marine Engineering)

X{axin'rum : 100 marirsTime : Three hoursAnswel ALL questions'

I'ART A -(L0Y'2= 20 marks)

1. T\Po forces of magmtude 20 N and 40 N are actins on a particle such that theansle between th" '*;:t ;;;'-ii#1 tr11e fSrces are acting arvav from theilil;;;i;i";" th"i"""'1t''''t and frnd its direction2. A force ft = (li -S.i +ll') N acts at A of co ordinates (f ' 3' 4) Determine the

moment offorce F about the co-ordinate axes'3. Find the product o{ lnertia (1t") about centroidal axis for the area formed by

substracting the "ir& of diameter 40 mm for the square of side B0 mm asshown in Fig Q' 3 C""t-'a "f "it"le coincicles with centroid of square

4.

ll,

6.

Fie. Q 3State the location of centroid of semicircle arc whose radius is r' rvith a sketch

A lirt has an 'pward accereration of 1 m/s2. what pressur-e u'i}r aman weighing

OOO N "*.t on the floor ol r he liiLl'l'1-re angular rotation in raclians of an accelerated flr'-wheel is gven byrt = 9- t'. Find its angular acceleralion r"hpn I ' l 6 s'


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.KI6c*-Jt,

7.

8.

CmI.L

o

A ball dropped from a heisht of 1.6 m on a floor rebounds to a height of 0.9 m,ind the co +fficient ofrestitution.A circular disc has a mass moment of inertia of 12 kg mz about its axis ofotation lf it is initia'y at rest' find i ts ^ang,-.lar velocity after 3 seconds, if it iscted upon by a torque of magnitude g00 N;.A car starts from rest with a constant acceleration of 4 mrs2- Determine theistance travelled in the 7th second.

10. Differentiate between Relative velocity and Resultant velocity.PARTB_(5x16=80marks)

11. (i) Determine the centroid of area.shown in Fig. e 11 (i) by taking momentofarea about the given aa _ axis and bb _ alis. (g)iLbt,o,

Fig. Q. 11. (i)(ii) The cross section of a culvert is shown in Fig. e 1l (ii).moment of inertia about the horizontal A _ A axis,7cm , , 3un,f.-_-->l*- 6a -S--N

Compute the(8)

-

$$

N 1215


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12 (a) *:3* 91i3"r* ?; ::* a'g::ffifJ;fJ:q'H::+?$ ":#0 kN is suspenoeo aL Ltr' Jv!"" -. .I-^ , i.-ad '.omhqr of the truss-of forces i"a""lI ";;ff of the three member of the truss'(Ref Fig Q' 12 (a)'

lok ^tpi.' O 12 (a)

Or

-->x(rl

8ao N

(8)

Fig. Q. 12 (b) (i)(it Given that the vector F =+i-Zi+3h; Q=2i+4j+5h and

R = ]i - j* Xfr ' D"ttt*ine the value of X for which the threevectors are coPlalar'r3 {a) (i) Determine whether rhe block *o*n^l ?,:;"'";#;#ltn:'T":d mass of 40 kg is in equilibrium antdirection "f il-ftil; f;tu Tuk" l" = 0 40 and p' = 0 30 ' (8)

Fig. Q. 13 (a) (i)3

o

N 1215


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(ii) Determine the mass moment of inertia of the composite body aboutZ-axis shown in Fig. Q. 13 (a) (ii). The mass density of the cylinderis 6000 kg;/m3 and the rectangular prism is 7000 kg/m3.v

Fig. Q. 13 (a) (ii)Or

Find the reactions at the supports A and BFig. Q. 13 (b) (i).of the beam shown in(10)

** f'

Fig, Q. 13 (b) (i)(it A flat belt rolls over a pulley of diameter D, making contact angleB when their respective tensions are { and 7r. Derive arelationship between the tensions, angle of contact and co-efficient

of friction p. Show that the diameter of the pulley is immaterial' (6)

,l__II

(1)b)go kx

rv, ->l+- z ", -ala'-7-^--+


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Water drips lrom a faucet ai the rate "l fi"" *:"n:- -p,-"1:^"ji::a) iltl'Z i;?i. ij"telrine the verticai separatioi.r between tworr5 Y ' ' * --' ' - a.,c attained a'elociiy of 3m/s'o rops lft^'ii-'lower drop n

h'Eo

Fig Q' 14 (a)Or

A 0.001 kg (rnass) bullet has a velocity of;';J;i";k""it'ood It comes to rest 0 002 s;;;;;'th" t"ttug" force that acteddistance Penetrat'ed bY it'(b) (i)

n'ltf-tl"=n"" to B parallel to the plane

to!-i.' O. 15 (aJOr

as shorvn ineonsecutive

1 krn/S as it enters aafter entering the blockon the bullet and the(s)

15. (a)

riir ln a policc investigalion of $irTillli :]r'=";";;::';'.lffiXjwhile in motion elong60 metres after the ;;"k";;;t; applied lf the co--effrcient offriction betwee. tl-r" t].". ""d tire paYement is estimated as 0 5'What was the ptobtb# "peed of the car just before the brakes wereaPPlied/ (B)Atwowhee}rirnsAandBweighingl00NandlsoNrespectivelyareallowed to roll down ut i"ait-t""a"pi^"? from rest as shown in Fig Q 15(a)'The incirned plane is "t eO" i" tLi ft"tizontal The lim A follorvs the riin Band the rims rvhen they are iust allowed to roll are 2 m bett'een centres'The exrernal radii ol th" ";;t

A and B are l00 mm and 150 mmresoectivelv Tl-rerr radii of gt;;;i"; ut" E0 mm and 130 mm respectivelyAssuming rolling without litpti"*' n"a the relative acceleration of A

ld 1,215


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(b) T\vo weights each of 100 N are suspended from a compound pulley asshown iJ Fig. Q. 15 (b) Find (i) angular acceleration of the pulley(ii) linear acceleration of the blocks A and B (iii) Tension in the string'Take weight of the pulley as 300 N and its radius of gtr'ration 0-25 m

Fig. Q. 15 (b)

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D 134B.E./B.Tech. DEGREE EXAMINATION, NO\|EMBER/DtrCEMBER 2005.

(Common to all branchestGE 1151 - ENGINEERING MECTIANICS

Time : Three hours Ma-rdmum : 100 marksAlsrver ALL questions-

PARTA-(10x2=20marks)State the principle of Transmissibility.Three. coplan-ar forces of magnitude p Newtons each are acting on a particle. Illheir lir,es ol action make equal angles with each other, shou, that the forcesare in equiiibrium.Stet" th" Varrgnon's theorom.Find the moment ol tl-re force of t5 NX a>iis about the point A (2, Z) . acting aiong the positive direction of

1.

2.

3.

4.

5. Distinguish between centroid and cenlre of gravily.6. Define product of inertia.7. Explain bnefly the two types of collision.E. If the distance r cm traveiled b1, a parlicle in I seconds is given byx = 20t2 + 501 + 19 , hnd the velocity and acceieration alter 3 seconds.

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